Expand the Trigonometric Expression (2x-3)(x-4)

$(2 x - 3) (x - 4)$

Step 1

Expand $(2 x - 3) (x - 4)$ using the FOIL Method.

Apply the distributive property.

$2 x (x - 4) - 3 (x - 4)$

Apply the distributive property.

$2 x \cdot x + 2 x \cdot - 4 - 3 (x - 4)$

Apply the distributive property.

$2 x \cdot x + 2 x \cdot - 4 - 3 x - 3 \cdot - 4$

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$2 (x \cdot x) + 2 x \cdot - 4 - 3 x - 3 \cdot - 4$

Multiply $x$ by $x$ .

$2 x^{2} + 2 x \cdot - 4 - 3 x - 3 \cdot - 4$

Multiply $- 4$ by $2$ .

$2 x^{2} - 8 x - 3 x - 3 \cdot - 4$

Multiply $- 3$ by $- 4$ .

$2 x^{2} - 8 x - 3 x + 12$

Subtract $3 x$ from $- 8 x$ .

$2 x^{2} - 11 x + 12$